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Abstract: We give a model-theoretic account for several results regarding sequences ofrandom variables appearing in Berkes and Rosenthal\cite{Berkes-Rosenthal:AlmostExchangeableSequences}. In order to do this,{itemize} We study and compare three notions of convergence of types in astable theory: logic convergence, i.e., formula by formula, metric convergenceboth already well studied and convergence of canonical bases. In particular,we characterise $\aleph 0$-categorical stable theories in which the last twoagree. We characterise sequences which admit almost indiscerniblesub-sequences. We apply these tools to $ARV$, the theory atomless randomvariable spaces. We characterise types and notions of convergence of types asconditional distributions and weak-strong convergence thereof, and obtain,among other things, the Main Theorem of Berkes and Rosenthal. {itemize}



Author: Itaï Ben Yaacov ICJ, Alexander Berenstein, C. Ward Henson UIUC

Source: https://arxiv.org/



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